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Experimental Investigations

Most of pioneering studies performed to investigate the seismic behavior of unanchored liquid storage tanks were experimental in nature because of the complexities associated with the analytical solution of the problem. The majority of these experiments were performed on small scale models. A pioneer work in this field was performed by Clough and his coworkers during a large experimental program with model tanks on the EERC shaking table. A broad tank, 12 ft in diameter by 6 ft in height, was investigated by D. Clough [36] and a few years later by Manos ([168], [171]). In addition, Manos and Clough ([174], [175]) presented the dynamic response results of an unanchored broad aluminum tank model of a similar size due to one horizontal component of the 1940 El Centro earthquake record applied with 0.5g peak acceleration. The tank base was free to uplift from either a rigid or a flexible base surface. The tank response was dominated by the uplift mechanism which varied nonlinearly with the intensity and frequency of input motions. For a rigid foundation, the coupling of uplift mechanism with out-of-round distortions resulted in high compressive axial membrane stresses developed over a narrow contact zone. For a more flexible foundation, lower compressive stresses, distributed more widely along the base of the tank wall, were observed. Also, for a less rigid foundation, large uplift accompanied by high levels of compressive hoop stresses on the uplifted part of the tank wall, and correspondingly large bending and membrane stresses in the bottom plate, were reported. They concluded that a realistic uplift mechanism prediction, out-of-round distortional response, foundation flexibility and a more realistic failure criterion should be incorporated in design procedures. They also recommended further experimental work to establish allowable values of buckling stresses suitable for use in the seismic design of such tanks. In a following work [173], they examined two cases of the behavior of tank models when subjected to lateral loads. In the first case, these loads were introduced by a static-tilt test. In the second case, the dynamic characteristics of the same model were examined by subjecting it to a variety of horizontal base motions.

In 1979, Clough et al [37] summarized results of an experimental study on tank models that started in 1975. Objectives of the study were to measure the actual behavior of two aluminum cylindrical tank models when subjected to realistic base motions, and to compare this behavior with predictions based on standard design procedures. They reported that due to the tank wall flexibility, impulsive hydrodynamic pressure component was amplified beyond the value expected in a rigid tank, and flexibility associated with the uplift mechanism drastically altered the entire tank behavior. Significant out-of-round displacements were observed in both tanks and were believed to be related to initial imperfections of the tank's geometry. It was noted that for the same input acceleration amplitude, shell displacement and stress amplitudes were much higher in unanchored tanks than those in anchored tanks. They also reported that for unanchored tanks, there was a poor correlation between predicted and observed results, and the unexpected behavior observed in these tests with respect to uplifting kinematics demonstrated the need for additional analytical studies of seismic response of unanchored tanks.

In addition to tests on broad tanks, tall tanks were also tested. In 1979, Clough and Niwa [38] reported the results of a static tilt test of a cylindrical liquid storage tank. The tilt test was carried out on the same aluminum tall tank model (7-3/4 ft by 15 ft) used earlier in previous shaking table tests performed by Niwa [204]. Results of typical design calculations were compared with the observed behavior, and it was noted that the unanchored tank tilted more and developed much greater axial stresses than were indicated by typical design procedures. Compressive stresses were concentrated over a much narrower contact zone than was expected, leading to an amplified peak stress. In a following work, Niwa and Clough [203] investigated the buckling of these tanks under earthquake loadings.

Small scale models were also tested experimentally. Ishida et al [127] performed a vibration test and a static tilt test on a small stainless steel tank model. In 1984, Shih and Babcock ([249], [250]) reported on an experimental project which was carried out to provide a better understanding of damages produced by the 1979 Imperial Valley earthquake to oil storage tanks. They studied the buckling behavior of a small unanchored tank model constructed of Mylar A sheet with a floating roof. The tank model was subjected to a single axis horizontal base excitation, and harmonic as well as simulated earthquake base motion. They found that buckling of the model was in reasonable agreement with field observations, and that floating roof had no effect on the buckling behavior. Following a comparison with API 650 design provisions, it was found that buckling predictions and tip over calculations of the code were conservative by over a factor of two. They also showed a marked difference between the response of anchored and unanchored tanks.

Tests on full scale models have also been attempted. It started in 1987 when Sakai et al [239] presented a static tilt test with a full scale tank model in order to investigate the uplift behavior of large size cylindrical liquid storage tanks. They made a comparison with theory and reported that experimental results did not agree with their theoretical analysis around the bottom of the tank. They concluded that the stress distribution around the shell-base corner and the contact condition between the bottom plate and the foundation should be considered carefully because of the complicated uplift behavior. In a following work, they carried out a static tilt tests ([236], [237], [238]) in order to investigate complicated uplifting phenomena in details. They have used such a big model as were not employed in the past studies. They reported that their model satisfied almost perfectly the similitude law to a large-scaled prototype tank, and consequently should grasp very well the fundamental behavior of actual tank's uplift.

In 1983, Cambra ([27], [28]) investigated the earthquake response behavior of an unanchored broad tank model, also 12 ft in diameter by 6 ft in height. The study included axial symmetric lift tests, static tilt tests and dynamic shaking table tests using both a rigid mortar as well as flexible rubber foundations. It was concluded that seismic response of tanks was significantly affected by the variation of foundation flexibility, and there was a strong correlation between the tank shell eccentricities created by fabrication imperfections and/or shell deformations and out-of-round response. An empirical tie element model representing the uplift behavior of the tank base plate was also described in order to improve design procedures for unanchored tanks. Wozniak and Mitchell's model [292] was modified by analyzing two elastic beams: one in the uplift region and the other in the contact region. Both beams were subjected to a transverse distributed load which produces longitudinal membrane forces. In contact region, the beam was assumed to be supported on a Winkler foundation. This was considered an improvement since it took into account both the membrane force and the bending moment at the beginning of the uplift region whereas, on a rigid foundation, there were no moments assumed at junction of uplift and contact regions. The membrane force was calculated by considering the strip beam as an extensible string with no longitudinal displacements allowed at its ends, and by assuming that the total load on the strip is carried only by membrane force. This membrane force was later introduced as a given longitudinal force in the linear equation of an elastic beam which is incompatible with the general equilibrium as the total load is already carried through the bending of the beam. In reality, part of the load carried by membrane effects of the plate and the remainder by bending effects. Only the elastic behavior of the plate was considered in contradiction to the valid assumption of the existence of plastic hinges. However, based on this model, it was found that both the wall uplift and the separation of the tank bottom plate occurred at values larger than what design codes anticipate for credible earthquake magnitudes.

Theoretical studies were also performed to support the static tilt test. Lau ([147], [148], [149]) adopted a general method for predicting the static tilt performance of a cylindrical liquid storage tank that is free to uplift. The base plate, subjected to both membrane tension and plate bending, was divided into contact and uplifted regions. Deformations of the bottom plate were evaluated by a Ritz-type method using iterations to determine the boundary of the contact region and full continuity was maintained with the tank wall. The cylindrical tank shell was analyzed by using Flugge thin shell theory and its stiffness was cast in a form comparable with that of the base plate for direct stiffness summation. The stiffening effects of the top rim wind girder and the bottom toe ring were also included. Friction exerted along the bottom edge of the shell still in contact with the platform was modeled by lateral support springs of a stiffness that was fine tuned to model frictional forces. Using this analytical approach, the responses of a broad and a tall model tank to various angles of tilt were evaluated and the results were compared with measured data. The differences in uplift behavior between the broad and tall tank models were discussed. Finally, the sensitivity of the uplift behavior to various parameters characterizing the tank system were studied.

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Next: Simplified Models Up: Evolution of Seismic Analyses Previous: Evolution of Seismic Analyses
A. Zeiny